C₂×#13823 #513537

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

6666 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 18 points:

(1,2);(3,4)(5,6)(11,12,14,13)(16,18);(4,6)(7,8,10,9);(11,12,14,13)(15,16)(17,18);(3,4)(5,6)(7,9,10,8)(11,13,14,12)

maximal subgroup of	C₂×#533088, C₂×#1494104, C₂×#534907, …
maximal normal subgroup of	C₂×#533088, C₂×#1494104, C₂×#534907, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420733);